Q. 17

# Show that the quadrilateral formed by the straight lines x – y = 0, 3x + 2y = 5, x – y = 10 and 2x + 3y = 0 is cyclic and hence find the equation of the circle.

Answer :

Solving the euations we get the coordinates of the quadrilateral.

Slope of = 1

Slope of CD = 1

AB||CD

Slope of BD = AC = - 1

AC||BD

So they form a rectangle with all sides = 90

The quadrilateral is cyclic as sum of opposite angles = 180.

Now, AD = diameter of the circle equation of the circle with extremities A(0, 0)&D(6, - 4) is

(x - 0)(x - 6) + (y - 0)(y + 4) = 0

x^{2} + y^{2} – 6x + 4y = 0

Rate this question :

Show that the quadrilateral formed by the straight lines x – y = 0, 3x + 2y = 5, x – y = 10 and 2x + 3y = 0 is cyclic and hence find the equation of the circle.

RS Aggarwal - MathematicsIf ( - 1, 3) and (∝, β) are the extremities of the diameter of the circle x^{2} + y^{2} – 6x + 5y – 7 = 0, find the coordinates (∝, β).

Find the equation of the circle which passes through the points A(1, 1) and B(2, 2) and whose radius is 1. Show that there are two such circles.

RS Aggarwal - MathematicsFind the equation of the circle concentric with the circle x^{2} + y^{2} – 6x + 12y + 15 = 0 and of double its area.